Measurement of the Communication Possibility of Service Requests for Multiservers in Parallel Connection in Cloud Computing Systems

Newly, growing amount of data‐demanding applications arrangement with continuous fluctuating data substances, have been investigated by many researchers recently. In these applications, the underlying data management system must support new types of the space‐time changing that indicates to the paths of the cloud computing system (CCS). The time‐space changing causes change in the dimension of data and, consequently, in the CCS. One of the solutions regarding this case is suggesting an integrated cloud computing system (ICCS). In this effort, we introduce a new ICCS, based on fractional formal operators, taking into account the symmetrical delay in it. This model is useful for higher dimensional data, moving data, and chaos data. Moreover, we employ a fractional differential method to discover the paths (outcomes) of the system by minimizing the cost function. The proposed system delivers a sequence of paths that converge to the optimal path. The theoretical technique is supported by the applications

Ulam stability for fractional differential equations in the sense of Caputo operator

In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDßzf(z)=G(f(z), cDázf(z),zf‘(z);z) 0<á<1<ß<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated

On the existence and uniqueness of solutions of a class of fractional differential equations

AbstractIn this paper, we investigate the existence and uniqueness of solutions for the following class of multi-order fractional differential equationsDβ1γ1,δ1⋯Dβnγn,δnu(t):=∏i=1nDβiγi,δiu(t):=Dβi,nγi,δiu(t)=f(t,u(t)),t∈[0,1],u(0)=0,∑i=1nδi⩽1,γi>0,βi>0,1⩽i⩽n, where Dβi,nγi,δi denotes the generalized Erdélyi–Kober operator of fractional derivative of order δi. Moreover, some properties concerning the positive, maximal, minimal, and continuation of solutions are obtained

Integral Operator Defined by k-th Hadamard Product

We introduce an integral operator on the class A of analytic functions in the unit disk involving k Æ’{ th Hadamard product (convolution) corresponding to the differential operator defined recently by Al-Shaqsi and Darus. New classes containing this operator are studied. Characterization and other properties of these classes are studied. Moreover, subordination and superordination results involving this operator are obtained

A New Method for the Economic Laws of Extinction Using the Fox-Wright-type Function

In this note, we deal with the possibility of optimal economic extinction. We employ the Fox-Wright-type function to characterize the probability of transference from optimal selection to the economic laws of extinction. For the extinction, we shall utilize the fractional Poisson process